From bbd356207fc8e45e7866b1be9ddc99a193d88f4e Mon Sep 17 00:00:00 2001
From: Dmitri Naumov <dmitri.naumov@ufz.de>
Date: Thu, 27 Feb 2020 15:02:14 +0100
Subject: [PATCH] [doc] Comparison of different Bishop's models.
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+size 65602
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+project = "RichardsMechanics/bishops_effective_stress_power_law.prj"
+author = "Dmitri Naumov"
+date = "2020-02-27"
+title = "Bishop's effective stress models comparison"
+weight = 153
+
+[menu]
+ [menu.benchmarks]
+ parent = "richards-mechanics"
+
++++
+
+{{< data-link >}}
+
+Two models for the Bishop's effective stress computation are presented; the
+power-law model, and saturation cut-off model. The models are:
+$$
+\chi(S_\mathrm{L}) = S_\mathrm{L}^{m_\chi}
+\qquad \mbox{and}\qquad
+\chi(S_\mathrm{L}) =
+ \chi = \begin{cases}
+ 1 & \mbox{for $S_\text{L} \geq S_\text{cutoff}$}
+ \\
+ 0 & \mbox{for $S_\text{L} < S_\text{cutoff}$.}
+ \end{cases}
+$$
+Simulation result shows different influence of the effective stress on the
+displacement. In the test the medium is desaturated and then saturated again,
+which causes shrinkage and expansion of the domain. Power law with exponents 1,
+1/5, and 5 and saturation cut-off at maximum liquid saturation of 0.95 are
+compared.
+{{< img src="../BishopsEffectiveStress.png" >}}
--
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